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Past exam of the mathematics course of the University of Cambridge / 2021 / ia / Paper 3 / 3B / b / ii / Solution

On the annulus the logarithmic term is allowed, so

u (r) = r^{4} + C lo g r + D .

The condition

u (1) = 1

gives

D = 0

, while

u (2) = 1

gives

16 + C lo g 2 = 1.

Therefore

u (r) = r^{4} - \frac{15 lo g r}{lo g 2} .

Solved by gpt-5.6-sol high.

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